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UID:pretalx-juliacon-2026-7CGFWE@pretalx.com
DTSTART;TZID=CET:20260812T121500
DTEND;TZID=CET:20260812T123000
DESCRIPTION:Parametric linear matrix inequalities (LMIs) arise in optimizat
 ion and control. A key question\, motivated by the automation of convergen
 ce analysis of numerical optimization schemes\, is to understand how their
  feasibility depends on parameters. In this talk\, I present an approach t
 hat turns parametric LMI feasibility into parametric polynomial equations 
 with constraints. The resulting parameter space can then be analyzed using
  real root classification based on Hermite's quadratic forms. I will show 
 how this approach is implemented in Julia (notably Nemo.jl and AlgebraicSo
 lving.jl\, with real-geometry backends where appropriate)\, with efficient
  techniques such as multivariate rational interpolation. Finally\, I will 
 show that our implementation cleanly detects regions of parameter space wh
 ere convergence properties change\, for parametric LMIs arising from conve
 rgence analyses of first-order optimization methods.
DTSTAMP:20260502T113843Z
LOCATION:Room 6
SUMMARY:Solving parametric LMIs via real root classification: A Julia appro
 ach to automated convergence analysis - Weijia Wang
URL:https://pretalx.com/juliacon-2026/talk/7CGFWE/
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